The market for simple centering mechanisms is large. The most common is a screw-driven type device such as found on a drill to center and clamp a drill bit. Another is on a lathe to chuck small parts. But when attempting to chuck (center and clamp) a workpiece that is large or very small, those types of chucks become bulky, heavy, or not feasible because of the micro-scale. A simple solution that is light weight, easy to handle, scalable to any size, and easy to build (even for holding a large workpiece) for lathe work is called a Longworth Chuck. Its concept is also currently used in the Medical and Aerospace fields. The key issue with the Longworth Chuck is that it is based on a constant curvature arc—a segment of a circle. This limits the size of objects that can be centered on a fixed size chuck and does not provide for a near constant perpendicular force resulting in workpiece chatter, or causing binding or mechanical interference if each slot is too long relative to the size of the chuck.
The Longworth Chuck is made by cutting constant radius slots into two plates. One plate is reversed and then the flat faces of the two plates are put together in an opposing manner such that their origin of their axis align. Clamps are inserted into the slots where the slots intersect at their outermost position in a manner, in some embodiments, that results in a rigid clamp when locked but can slide within the slots as the location of the intersection moves. As one plate is counterrotated relative to the other plate centrically around a center bushing, the clamps are forced inward or outward depending on the relative rotation between the two plates. Thus, the slot of one plate pushes the clamp inward or outward along the slot of the opposing plate. As long as the slot that is pushing against the clamp is fairly perpendicular to the direction that the clamp is supposed to move, the mechanism works well. But when the pushing slot becomes less perpendicular more force is required to move the clamp and the mechanism can jam or decreases the holding-force when locked. To mitigate this issue, the length of each slot is limited in length, which limits the size of the workpiece that can be centered and held. Also, because perpendicularity is not present where the two slots intersect (except at possibly one point) and the intersect angle increases as it moves inward, the slot clamp-up force varies causing workpiece chatter. This limits its application, reliability, and use. The problem is large enough that some machinists avoid use of the Longworth chuck and turn to other more complicated and less versatile chuck methods.
Thus a system that keeps the slots relatively perpendicular was needed to:                Keep the forces to move the clamp inward and outward at a minimum and prevent binding or mechanical interference, especially during the final clamp-up when the clamps engage and hold the workpiece.        Allow centering/holding chucks to be more versatile by being able to center and hold a greater variety of workpiece sizes and shapes.        Greater clamp-up force to hold the workpiece to allow greater holding forces that decrease workpiece chatter, allow faster milling rates, and/or allow deeper cutting depths.        